Local well-posedness of solutions to the boundary layer equations for 2D compressible flow

作者：Fan, Long; Ruan, Lizhi^*; Yang, Anita

来源：Journal of Mathematical Analysis and Applications, 2021, 493(2): 124565.

DOI：10.1016/j.jmaa.2020.124565

• Boundary layer equations
• Compressible isentropic flow
• Local well-posedness
• Energy method
• Maximum principle

In this paper, we give a new direct proof by energy method for the local well-posedness of the boundary layer equations for two-dimensional compressible isentropic flow with no-slip boundary condition. It requires less compatibility conditions than the previous result using Nash-Moser-Hormander iteration scheme and linear energy estimates. It shows that maximum principle works for boundary layer equations so that the weighted L-infinity estimates on the lower order terms can be obtained.